Question

a right circular cone is of height 8.4 and radius of its base is 2.1 CM.It is melted and recast into a sphere. Find radius of the Sphere​

Answer 1

Answer:

R=2.1

Step-by-step explanation:

We have.

r= radius of the base of the cone=2.1cm

h= height of the cone=8.4cm

Volume of the cone =

3

1

πr

2

h=

3

1

×π×(2.1)

2

×8.4cm

3

Let R cm be the radius of the sphere obtained by recasting the melted cone.

Then volume of the sphere =

3

4

πR

3

Since the volume of the material in the form of cone and sphere remains the same

∴

3

4

πR

3

=

3

1

×π×(2.1)

2

×(8.4)

⇒R

3

=

4

(2.1)

2

×8.4

=(2.1)

3

⇒R=2.1cm

Answer 2

$\fbox \pink {A} \fbox \blue {N} \fbox \purple {S} \fbox \green {W} \fbox \red {E} \fbox \orange {R}$

Given,

radius of the base of the cone=2.1cm

height of the cone=8.4cm

Volume of the cone =

$\frac{1}{3} \pi {r}^{2} h = \frac{1}{3} \times \pi \times {(2.1)}^{2} \times {8.4cm}^{3}$

Let R cm be the radius of the sphere obtained by recasting the melted cone.

Then volume of the sphere =

$\frac{4}{3}\pi {r}^{3}$

Since the volume of the material in the form of cone and sphere remains the same

∴

$\frac{4}{3} \pi {r}^{3} = \frac{1}{3} \times \pi \times {(2.1)}^{2} \times(8.4)$

⇒

${r}^{3} = \frac{ {(2.1)}^{2} \times 8.4 }{4} = ( {2.1)}^{3} ⇒r = 2.1cm$

$\textit{Hope this helps you}$